The Non-Euclidean Configuration K
The configuration K is inadmissible in the Euclidean space and we may assume that it belongs to a non-Euclidean, linearly connected space L3, the geometry of which is determined by the thermal distorsions θ L (λ) . The space L3 should reduce to the Euclid
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RASTKO STOJANOVIC
t
UNIVERSITY OF BELGRADE
NONLINEAR THERMOELASTICITY
LECTURES HELD AT THE DEPARTMENT OF MECHANICS OF SOLIDS JULY 1972
SPRINGER-VERLAG WIEN GMBH 1972
This work is subject to copyright Ali righ ts are reserved, whether the whole or part of the material is concemed specifically those of translation., reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © Springer-Verlag Wien 1972 Originally published by Springer-Verlag Wien-New York in 1972
ISBN 978-3-211-81200-6 ISBN 978-3-7091-2856-5 (eBook) DOI 10.1007/978-3-7091-2856-5
Preface
I am mostZ.y
indebted to the authori-
ties of CISM, and in partiaular to the Reators and to the Searetary General. for giving me the opportunity to give this aourse of six Z.eatures on non-Z.in ear thermoeZ.astiaity. Having some points of view in this fieZ.d of researah whiah are not aommon in the generaZ. theories of thermo-meahanias, this is for me a good opportunity to deveZ.op systematiaaZ.Z.y the
o.~
gument and to aompare different approaahes to the probZ.em of thermal. stresses. The avaiZ.abZ.e time and spaae do not permit me to enter into many interesting probZ.ems of non-Z.inear thermomeahanias and I
r~
striated the aonsiderations onZ.y to the derivation of the aonstitutive reZ.ations and to their approxim~ tion by reZ.ations invoZ.ving the seaond-order terms. My aoZ.aborators and former students, Miss S. MiZ.anovic and Dr. D. BZ.agojevic heZ.ped me in the preparation of this manuscript and I appreciate their assistence very much. April. 24, 1972 BeLgrade
R. Stojanovic
lntroduction
In the contemporary mechanics it is impossible to consider mechanical phenomena indipendently of the laws of thermodynamics even when the idealized processes like elastici ty are considered. In thermoelasticity this coupling of mechan ical and thermal fields becomes only accentuated. In the classical, linear thermoelasticity the influence of temperatureis introduced into the stress-strain relations through the thermal strain tensor and the so obtained Neumann-Duhamel law simply replaces Hooke's law. If a linear heat conduction law, say Fourier 1 s law, is added to the stress relations, the system of constitutive equations is completed. For the majority of eng! neering applications the linear theory gives sufficiently good results. The development of the non-linear continuum
m~
chanics automatically rises the problern of a general approach to thermo-mechanical phenomena. The fundamental set of equations is again represented by the heat conduction law and the stress relation, and the main restrictions upon these relations are imposed by the laws of thermodynamics. However, the energy functions which appear in such general formulations are consid erably more complicated then in the linear theory. Without entering into details of the development
Introduction
6
of the non-linear thennoelastici ty we shall mention here some of the most important contributions. In the already classical work
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